Simplify the following expression: $n = \dfrac{7q^2 + 35q - 168}{q + 8} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $7$ , so we can rewrite the expression: $ n =\dfrac{7(q^2 + 5q - 24)}{q + 8} $ Then we factor the remaining polynomial: $q^2 + {5}q {-24} $ ${8} {-3} = {5}$ ${8} \times {-3} = {-24}$ $ (q + {8}) (q {-3}) $ This gives us a factored expression: $\dfrac{7(q + {8}) (q {-3})}{q + 8}$ We can divide the numerator and denominator by $(q - 8)$ on condition that $q \neq -8$ Therefore $n = 7(q - 3); q \neq -8$